They are refering to 2 channel to 5.1 surround decoders. They are completely different than 2 channel to 3 speaker matrixes. Usually the are not linear but employ all kinds of nonlinear processing to try to create the missing information for 5 speakers.

However if we have 3 speakers and they are in front the situation is very much easier.

Hmm... good point! I've got a BruteFIR-based DSP with a web interface (to add/configure filters) here, so linear-matrixing is very easy to implement. All I need is an extra speaker. Which is sort of a problem at the moment.

I've got a BruteFIR-based DSP with a web interface (to add/configure filters) here, so linear-matrixing is very easy to implement. All I need is an extra speaker. Which is sort of a problem at the moment.

For starters there is no need for DSP. All you need is stereo amplifier with common ground and some wire and use some of the passive schemes from this thread. For this experiment 3 speakers is a must, though. Looks like you have another task for the new year

No I mean what is "the standard linear-matrix upmixing" method you did not find performing well ?

If I'm not mistaken it was Dolby Pro Logic (or perhaps Pro Logic II). I think the receiver was a Marantz SR-7000, but I'm not sure. It was about five years ago. I am still curious about trying centre derivations and/or ambience extraction methods, so yes, I have a new task for this year

It was Dolby Pro Logic think, or possibly Pro Logic II. It was about five years ago. I am still curious about trying centre derivations and/or ambience extraction methods, so yes, I have a new task for this year

Also please try the side wall setup I've shown. There's something "special" about this.
I've had my Nathan's set up in a standard ±30° stereo triangle away from the walls, with a 45° toe-in. The loud contralateral reflection had a detrimental effect on imaging. With the speakers directly at the wall, the problem is completely gone. The resulting reflection pattern seems to aid reproduction (spaciousness and depth).
One simply needs to experiment with toe-in to get the ratio between direct sound and first reflections right. I've also found that the distance from listener to speakers needs to be exactly the same and it's important the whole setup is symmetrical.
The whole front wall in my room is damped. Not sure how important this is.

Apart from all the theorizing and “should works” and "special cases", is there any simple matrix technique that will, with a majority (or at least a substantial minority) of recordings currently available and over a reasonable sized listening area (not the “one chair in an otherwise empty room”) provide a consistent improvement in overall imaging and center channel stability when compared to plain old “standard” two channel reproduction?

Is there anything, that is, that you can simply “plug in”, add a center speaker, and expect “better” sound most of the time, and degraded sound rarely if at all?

Apart from all the theorizing and “should works” and "special cases", is there any simple matrix technique that will, with a majority (or at least a substantial minority) of recordings currently available and over a reasonable sized listening area (not the “one chair in an otherwise empty room”) provide a consistent improvement in overall imaging and center channel stability when compared to plain old “standard” two channel reproduction?

Is there anything, that is, that you can simply “plug in”, add a center speaker, and expect “better” sound most of the time, and degraded sound rarely if at all?

If we include head turning and/or off center listeners, then any method is an improvement over the standard 2 speaker stereo triangle.